|
In statistics, Ward's method is a criterion applied in hierarchical cluster analysis. Ward's minimum variance method inaccurate, see talk is a special case of the objective function approach originally presented by Joe H. Ward, Jr.〔Ward, J. H., Jr. (1963), "Hierarchical Grouping to Optimize an Objective Function", ''Journal of the American Statistical Association'', 58, 236–244.〕 Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This objective function could be "any function that reflects the investigator's purpose." Many of the standard clustering procedures are contained in this very general class. To illustrate the procedure, Ward used the example where the objective function is the error sum of squares, and this example is known as ''Ward's method'' or more precisely ''Ward's minimum variance method''. ==The minimum variance criterion== Ward's minimum variance criterion minimizes the total within-cluster variance. To implement this method, at each step find the pair of clusters that leads to minimum increase in total within-cluster variance after merging. This increase is a weighted squared distance between cluster centers. At the initial step, all clusters are singletons (clusters containing a single point). To apply a recursive algorithm under this objective function, the initial distance between individual objects must be (proportional to) squared Euclidean distance. The initial cluster distances in Ward's minimum variance method are therefore defined to be the squared Euclidean distance between points: : Note: In software that implements Ward's method, it is important to check whether the function arguments should specify Euclidean distances or squared Euclidean distances. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ward's method」の詳細全文を読む スポンサード リンク
|